Thats not really how morals are defined. That is just one oversimplified and fairly self serving definition of ethics.
But lets try this with your own view point: Try pondering the question you posed:
>what are morals and these 'should's you describe meant for?
Now since you believe common values help us get along, and you therefore believe that forms the basis of ethical decision, then your question needs to be:
"What common values do other people hold that may be different to mine?"
It may come as a shock to you, that there is whole world of people and even animals and insects, that don't share your views - that see the world through totally different eyes. If they don't contribute to your idea of a common value, does that make them worthless and irrelevant to the world, the world they live in.
By stomping on the cockroach (for no reason beyond what you like and don't like) - you are saying it has no value in your life, and therefore should not exist.
To be honest, this isn't about morality - its about having a basic respect for anything that lives. Why, given the chance, would you not have this respect?
(Edited: formatting)